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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The $p$-adic log gamma function and $p$-adic Euler constants
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by Jack Diamond PDF
Trans. Amer. Math. Soc. 233 (1977), 321-337 Request permission


We define ${G_p}$, a p-adic analog of the classical log gamma function and show it satisfies relations similar to the standard formulas for log gamma. We also define p-adic Euler constants and use them to obtain results on $G{’_p}$ and on the logarithmic derivative of Morita’s ${\Gamma _p}$.
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  • Jean Fresnel, Nombres de Bernoulli et fonctions $L$ $p$-adiques, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 2, 281–333 (1968) (French). MR 224570, DOI 10.5802/aif.271
  • Kenkichi Iwasawa, Lectures on $p$-adic $L$-functions, Annals of Mathematics Studies, No. 74, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0360526, DOI 10.1515/9781400881703
  • M. Krasner, Rapport sur le prolongement analytique dans les corps valués complets par la méthode des éléments analytiques quasi-connexes, Table Ronde d’Analyse non archimédienne (Paris, 1972) Bull. Soc. Math. France, Mém. No. 39–40, Soc. Math. France, Paris, 1974, pp. 131–254 (French). MR 0385168, DOI 10.24033/msmf.166
  • Tomio Kubota and Heinrich-Wolfgang Leopoldt, Eine $p$-adische Theorie der Zetawerte. I. Einführung der $p$-adischen Dirichletschen $L$-Funktionen, J. Reine Angew. Math. 214(215) (1964), 328–339 (German). MR 163900
  • D. H. Lehmer, Euler constants for arithmetical progressions, Acta Arith. 27 (1975), 125–142. MR 369233, DOI 10.4064/aa-27-1-125-142
  • Y. Morita, A p-adic analog of the T function, (to appear). N. Nielsen, Die Gammafunktion, Bände I, II, Chelsea, New York, 1965. MR 32 #2622.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 233 (1977), 321-337
  • MSC: Primary 12B40; Secondary 33A15
  • DOI:
  • MathSciNet review: 0498503